Learning Inductive Riemannian Manifold in Abstract Form by Modeling Embedded Dynamical System

Article type: Research Article

Authors: Bavafaye Haghighi, Elham^; | Rahmati, Mohamad | Palm, Guenther | Shiry Ghidary, Saeed

Affiliations: Computer Engineering and Information Technology Department, Amirkabir University of Technology, Tehran, Iran, e-mail: [email protected], [email protected] | Institute of Neural Information Processing, University Ulm, Ulm, Germany, e-mail: [email protected], [email protected]

Note: [] Corresponding author.

Abstract: Manifold learning algorithms do not extract the structure of datasets in an abstract form or they do not have high performance for complex data.In this paper, a method for Learning an Inductive Riemannian Manifold in Abstract form (LIRMA) is presented in which the structure of patterns is determined by solving the embedded dynamical system of the patterns. In order to model corresponding system, the true sequence of patterns is estimated using a topology preserving method. LIRMA has the advantage of being an inductive method with low complexity. Additionally, it is a topology preserving method with respect to quantitative measures.

Keywords: learning inductive Riemannian manifold in abstract form (LIRMA), embedded dynamical system, underlying structure of dataset, continues-invertible-smooth mapping

Journal: Informatica, vol. 25, no. 3, pp. 361-384, 2014